Suppose that a and b are integers, a ≡ 7 (mod 19), and b ≡ 5 (mod 19), Find the integer c with 0 ≤ c ≤ 18 such that: 12. (a − b) ≡ c mod 19 13. (7a + 3b) ≡ c mod 19 14. (2a2 + 3b2) ≡ c mod 19

Suppose that a and b are integers, a ≡ 7 (mod 19), and b ≡ 5 (mod 19), Find the integer c with 0 ≤ c ≤ 18 such that: 12. (a − b) ≡ c mod 19 13. (7a + 3b) ≡ c mod 19 14. (2a2 + 3b2) ≡ c mod 19

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Suppose that a and b are integers, a ≡ 7 (mod 19), and b ≡ 5 (mod 19), Find the integer c with 0 ≤ c ≤ 18 such that:

12. (a − b) ≡ c mod 19

13. (7a + 3b) ≡ c mod 19

14. (2a² + 3b²) ≡ c mod 19

15. (a³ + 4b³) ≡ c mod 19

please show your solutions :)

I've already seen other answers to the problems but I'm unsure if that's correct pls help

v. Suppose that a and b are integers, a - 7 (mod 19), and b = 5 (mod 19). Find
the integer c with 0scs 18 such that:
12. (a – b) = c mod 19
13. (7a + 3b) = c mod 19
14. (2a? + 3b?) = c mod 19
15. (a³ + 4b3) = c mod 19

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